A Spin-Statistics Theorem for Certain Topological Geons

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral abelian geons do satisfy a spin-statistics correlation if they are described by a wave function which is given by a functional integral over metrics on a particular four-manifold. This manifold describes a topology changing process which creates a pair of geons from $R^3$.Comment: 21 pages, Plain TeX with harvmac, 3 figures included via eps

Energy extremality in the presence of a black hole

We derive the so-called first law of black hole mechanics for variations about stationary black hole solutions to the Einstein--Maxwell equations in the absence of sources. That is, we prove that $\delta M=\kappa\delta A+\omega\delta J+VdQ$ where the black hole parameters $M, \kappa, A, \omega, J, V$ and $Q$ denote mass, surface gravity, horizon area, angular velocity of the horizon, angular momentum, electric potential of the horizon and charge respectively. The unvaried fields are those of a stationary, charged, rotating black hole and the variation is to an arbitrary `nearby' black hole which is not necessarily stationary. Our approach is 4-dimensional in spirit and uses techniques involving Action variations and Noether operators. We show that the above formula holds on any asymptotically flat spatial 3-slice which extends from an arbitrary cross-section of the (future) horizon to spatial infinity.(Thus, the existence of a bifurcation surface is irrelevant to our demonstration. On the other hand, the derivation assumes without proof that the horizon possesses at least one of the following two (related)properties: ($i$) it cannot be destroyed by arbitrarily small perturbations of the metric and other fields which may be present, ($ii$) the expansion of the null geodesic generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil

From Green Function to Quantum Field

A pedagogical introduction to the theory of a gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function $W(x,y)=\langle\phi(x)\phi(y)\rangle$ regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at $W(x,y)$ starting from nothing but the retarded Green function $G(x,y)$. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished "vacuum" or "ground state", and to recognize some interesting formal relationships, including a general condition on $W(x,y)$ expressing zero-entropy or "purity".Comment: plainTeX, 29 pages, 7 figures. Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/157.G2f.pdf (or wherever my home-page may be, such as http://www.physics.syr.edu/~sorkin/some.papers/

Discreteness and the transmission of light from distant sources

We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to lengths and durations - or more specifically, replacing the Lorentzian manifold with an underlying discrete structure - need not disrupt the usual dynamics of propagation.Comment: 16 pages, 1 figure. Version 2: reference adde

To What Type of Logic Does the "Tetralemma" Belong?

Although the so called tetralemma might seem to be incompatible with any recognized scheme of logical inference, its four alternatives arise naturally within the anhomomorphic logics which have been proposed in order to accommodate certain features of microscopic (i.e. quantum) physics. This suggests that the possibility of similar, "non-classical" logics might have been recognized in India at the time when Buddhism arose.Comment: plainTeX, 10 pages, no figures. Added references, revised first appendix, edited for clarity. Most current version is available at http://www.pitp.ca/personal/rsorkin/some.papers/135.catuskoti.pdf} (or wherever my home-page may be